Evaluate the following: `\ (sqrt(3)+1)^5-(sqrt(3)-1)^5`

Evalute: (sqrt(3)+1)^(5) -(sqrt(3)-1)^(5)

(3)/(sqrt(3)+1)+(5)/(sqrt(3)-1)

Evaluate the following limit: (lim)_(x rarr1)(sqrt(3+x)-sqrt(5-x))/(x^(2)-1)

Given sqrt(2)=1.414, sqrt(3)=1.732, sqrt(5)=2.236 , find the value, correct to three decimals of the following (1-sqrt(3))/(sqrt(5)-sqrt(2))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Evaluate the following limit: (lim)_(x rarr1)(sqrt(5x-4)-sqrt(x))/(x^(3)-1)

(1)/(4sqrt(3)-3sqrt(5))

If both a and b are rational numbers,find the values of a and b in each of the following equalities :(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3)( ii) (3+sqrt(7))/(3-sqrt(7))=a+b sqrt(7)(5+2sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)( iv) (5+sqrt(3))/(7-sqrt(3))=47a+sqrt(3)b(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+b sqrt(15) (iv) (sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-b sqrt(3)

Evaluate the following limits: lim_(xrarr4)((3-sqrt(5+x))/(1-sqrt(5-x)))